双层预紧式六维力传感器基础理论与应用研究
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摘要
随着科学技术的迅速发展，传感器技术已经广泛应用于测量、控制及信息等领域，并且已成为高新技术的核心之一。在各种传感器中，六维力传感器以其能够检测空间六维力和力矩的全部信息而成为非常重要的一类传感器，并在航空航天、机器人、汽车制造、生物医疗等领域都有着广阔的应用前景。本文针对一种双层预紧式六维力传感器，主要对设计理论、标定实验以及传感器应用等方面进行深入的研究，为设计具有自主知识产权高精度的六维力传感器及其实用化奠定理论和实验基础。主要研究内容如下：
提出一种双层预紧式多分支六维力传感器，应用凸分析理论确定了该传感器结构可行的分支数目；建立了双层预紧式多分支六维力传感器的数学模型，应用螺旋理论推导得到作用在传感器上的六维力与测量分支轴向力之间的静力映射矩阵解析表达式。
系统推导了双层预紧式多分支六维力传感器静力分配问题。由于传感器为超静定结构，通过引入分支刚度加权广义逆等概念，求解了测量分支反作用力解的唯一形式，并对其物理意义进行讨论；将测量分支轴向力分解为两部分，其中一部分由作用在传感器上的外力产生，另一部分由初始预紧力产生；在此基础上，采用线性变换的方法确定了保证传感器结构稳定测量的初始预紧力大小；最后通过数值算例和实验验证了上述推导的正确性。
提出一种基于设计量程来确定六维力传感器结构参数的优化方法，建立了传感器在量程范围内受力时最大测量分支轴向力与结构参数之间的关系，并绘制出最大轴向力随结构参数的变化曲线，得到当最大轴向力取得最小值时的结构参数；分别对双层预紧式七分支和八分支六维力传感器进行结构参数优化；依据所优化的结构参数，完成双层预紧式七分支六维力传感器的结构设计，研制出六维力传感器系统样机。
研制了六维力传感器标定实验台，基于LabVIEW开发了六维力传感器静态标定软件；推导了六维力传感器线性度、重复性和回程误差性能指标的标定算法；采用多点加载法在量程范围内对传感器各维力/力矩进行逐级加载，经过对实验数据的处理，得到了传感器的各静态性能指标。实验结果表明该传感器具有较高的测量精度。
对并联结构六维力传感器误差来源与提高精度的方法进行研究，分析了并联式六维力传感器测量分支轴向变形对其测量精度的影响；推导了传感器应用中受力端重力对其测量精度的影响及补偿算法；分析预紧力对预紧式六维力传感器测量精度的影响，并提出通过增大预紧力来减小测量误差的方法。
应用螺旋理论和多自由度系统振动力学理论，建立了双层预紧式多分支六维力传感器的振动力学简化模型，推导得到了系统的运动微分方程；对系统运动微分方程进行求解，得到了系统在初始激励下响应的解析表达式，以及传感器的各阶固有频率值。采用阶跃信号响应法对传感器进行动态标定实验研究，得到了传感器的各阶固有频率，所得实验结果与理论计算、仿真结果一致。
针对曲面跟踪和轴孔装配两种典型的运动模型，进行六维力传感器应用研究。考虑广义六维力的三种形式，指出六维力传感器实际测量中所存在的局限性；规划了两种运动模型的运动过程，并推导基于六维力传感器检测信息的反馈控制算法；搭建了机器人力控制实验平台，依据力反馈控制算法规划了控制流程并编写运动控制软件；最后完成了曲面跟踪和轴孔装配两种力反馈控制实验。
With the rapid development of science and technology, sensor technology has beenwidely used in the fields of measurement, control and information, and has become oneof the cores of the high-tech. In all kinds of sensors, the six-axis force/torque sensor isone kind of the most important sensors as it can measure the six-dimensional force andmoment information in the space, and has broad application prospects in the field ofaerospace, robotics, automotive manufacturing and biomedical. This paper presents thein-depth research on the design theory, calibration experiments, as well as applications ofa double-layer pre-stressed six-axis force sensor, and builds the theoretical andexperimental basis for the design and application of high-precision six-axis force sensorwith independent intellectual property rights. The main contents of this paper are asfollows:
A double-layer and pre-stressed six-axis force sensor with multiple limbs isproposed, and the viable number of the measuring limbs of the sensor structure isanalyzed by using the theory of convex analysis. The mathematical model of thedouble-layer and pre-stressed six-axis force sensor is built, and the static mapping matrixbetween the six-axis force/torque applied on the sensor and the axial force on themeasuring limbs is derived out using screw theory.
The problem of force distribution of the double-layer and pre-stressed six-axis forcesensor is derived systematically. Because the structure of the sensor is staticallyindeterminate, the solution of the reacting force on the measuring limbs is solved byintroducing the concept of weighted generalized inverse of limb’s stiffness, and thephysical meanings of the calculation results are discussed. The forces on the measuringlimbs are decomposed into two parts, one is produced by the external force and the otheris related to the pre-tightening force. On the above basis, the pre-tightening force, whichcan ensure the sensor structure stably measure, is determined by a linear transformationmethod. Finally, the numerical example and experiment verify the correctness of theabove derivation.
A method to optimize the structure parameters of the six-axis force sensor isproposed based on the design measurement range. The relationship between themaximum axial force of measuring limbs and the structural parameters of the sensorwithin the full scales of force/torque applied is established. The curves of the maximumaxial force and the structural parameters are drawn, and the optimized structureparameters are obtained when the maximum axial force achieves the minimum. Thestructural parameter optimizations of double-layer pre-stressed seven-limb andeight-limb six-axis force sensors are carried out respectively. Based on the optimizedstructure parameters, the structural design of the seven-limb six-axis force sensor iscompleted, and the prototype of the sensor system is manufactured.
The calibration device for six-axis force sensor is manufactured and the static anddynamic calibration software is developed based on LabVIEW. The linearity,repeatability and hysteresis error of six-axis force sensor are derived. A multi-pointloading method to apply the loading force on each dimension step by step in the fullscales of force and torque is adopted. The static calibration experiments of sensorprototype are carried out, and the static performance indices of the sensor are obtained byprocessing the experimental data. The experimental result shows that the sensorprototype possesses good static performance.
Sources of measuring error of the parallel six-axis force sensor and the method toimprove the accuracy are studied. The influence of the axial deformation of themeasuring limbs to the measurement accuracy of parallel six-axis force sensor isanalyzed. The influence and compensation algorithm of the gravity of the robot’s endeffector when sensor applications are deduced. The influence of the pre-tightening forceto the measurement accuracy of pre-stressed six-axis force sensor is analyzed and amethod to reduce the measuring error by increasing the pre-tightening force is proposed.
By using screw theory and multi-degree-of-freedom system vibration mechanics, thevibration system simplified model of the double-layer and pre-stressed six-axis forcesensor is established, and the motion differential equation of the vibration system isdeduced. The response of the system in the initial excitation and the natural frequenciesof the sensor are obtained by solving the differential equations of motion. The dynamic calibration experiments are also carried out using the step signal response method, andthe natural frequency of the sensor is obtained. The experimental results are consistentwith the theoretical calculations and simulation.
The application research of six-axis force sensor is carried out based on two typicalmotion model of surface tracking and peg-in-hole assembly. The inadequacy of thesensor when measures the six-axis force online is pointed out by considering the threeforms of the generalized six-dimensional force/torque. The trajectories of the two motionmodels are planned, and the feedback control algorithm based on the measuringinformation of six-axis force sensor is deduced. The robot force control experimentalsystem is set up, and the control flow and motion control software based on the feedbackalgorithm are completed. Finally, the force feedback control experiments of surfacetracking and peg-in-hole assembly are carried out.
提出一种双层预紧式多分支六维力传感器，应用凸分析理论确定了该传感器结构可行的分支数目；建立了双层预紧式多分支六维力传感器的数学模型，应用螺旋理论推导得到作用在传感器上的六维力与测量分支轴向力之间的静力映射矩阵解析表达式。
系统推导了双层预紧式多分支六维力传感器静力分配问题。由于传感器为超静定结构，通过引入分支刚度加权广义逆等概念，求解了测量分支反作用力解的唯一形式，并对其物理意义进行讨论；将测量分支轴向力分解为两部分，其中一部分由作用在传感器上的外力产生，另一部分由初始预紧力产生；在此基础上，采用线性变换的方法确定了保证传感器结构稳定测量的初始预紧力大小；最后通过数值算例和实验验证了上述推导的正确性。
提出一种基于设计量程来确定六维力传感器结构参数的优化方法，建立了传感器在量程范围内受力时最大测量分支轴向力与结构参数之间的关系，并绘制出最大轴向力随结构参数的变化曲线，得到当最大轴向力取得最小值时的结构参数；分别对双层预紧式七分支和八分支六维力传感器进行结构参数优化；依据所优化的结构参数，完成双层预紧式七分支六维力传感器的结构设计，研制出六维力传感器系统样机。
研制了六维力传感器标定实验台，基于LabVIEW开发了六维力传感器静态标定软件；推导了六维力传感器线性度、重复性和回程误差性能指标的标定算法；采用多点加载法在量程范围内对传感器各维力/力矩进行逐级加载，经过对实验数据的处理，得到了传感器的各静态性能指标。实验结果表明该传感器具有较高的测量精度。
对并联结构六维力传感器误差来源与提高精度的方法进行研究，分析了并联式六维力传感器测量分支轴向变形对其测量精度的影响；推导了传感器应用中受力端重力对其测量精度的影响及补偿算法；分析预紧力对预紧式六维力传感器测量精度的影响，并提出通过增大预紧力来减小测量误差的方法。
应用螺旋理论和多自由度系统振动力学理论，建立了双层预紧式多分支六维力传感器的振动力学简化模型，推导得到了系统的运动微分方程；对系统运动微分方程进行求解，得到了系统在初始激励下响应的解析表达式，以及传感器的各阶固有频率值。采用阶跃信号响应法对传感器进行动态标定实验研究，得到了传感器的各阶固有频率，所得实验结果与理论计算、仿真结果一致。
针对曲面跟踪和轴孔装配两种典型的运动模型，进行六维力传感器应用研究。考虑广义六维力的三种形式，指出六维力传感器实际测量中所存在的局限性；规划了两种运动模型的运动过程，并推导基于六维力传感器检测信息的反馈控制算法；搭建了机器人力控制实验平台，依据力反馈控制算法规划了控制流程并编写运动控制软件；最后完成了曲面跟踪和轴孔装配两种力反馈控制实验。
With the rapid development of science and technology, sensor technology has beenwidely used in the fields of measurement, control and information, and has become oneof the cores of the high-tech. In all kinds of sensors, the six-axis force/torque sensor isone kind of the most important sensors as it can measure the six-dimensional force andmoment information in the space, and has broad application prospects in the field ofaerospace, robotics, automotive manufacturing and biomedical. This paper presents thein-depth research on the design theory, calibration experiments, as well as applications ofa double-layer pre-stressed six-axis force sensor, and builds the theoretical andexperimental basis for the design and application of high-precision six-axis force sensorwith independent intellectual property rights. The main contents of this paper are asfollows:
A double-layer and pre-stressed six-axis force sensor with multiple limbs isproposed, and the viable number of the measuring limbs of the sensor structure isanalyzed by using the theory of convex analysis. The mathematical model of thedouble-layer and pre-stressed six-axis force sensor is built, and the static mapping matrixbetween the six-axis force/torque applied on the sensor and the axial force on themeasuring limbs is derived out using screw theory.
The problem of force distribution of the double-layer and pre-stressed six-axis forcesensor is derived systematically. Because the structure of the sensor is staticallyindeterminate, the solution of the reacting force on the measuring limbs is solved byintroducing the concept of weighted generalized inverse of limb’s stiffness, and thephysical meanings of the calculation results are discussed. The forces on the measuringlimbs are decomposed into two parts, one is produced by the external force and the otheris related to the pre-tightening force. On the above basis, the pre-tightening force, whichcan ensure the sensor structure stably measure, is determined by a linear transformationmethod. Finally, the numerical example and experiment verify the correctness of theabove derivation.
A method to optimize the structure parameters of the six-axis force sensor isproposed based on the design measurement range. The relationship between themaximum axial force of measuring limbs and the structural parameters of the sensorwithin the full scales of force/torque applied is established. The curves of the maximumaxial force and the structural parameters are drawn, and the optimized structureparameters are obtained when the maximum axial force achieves the minimum. Thestructural parameter optimizations of double-layer pre-stressed seven-limb andeight-limb six-axis force sensors are carried out respectively. Based on the optimizedstructure parameters, the structural design of the seven-limb six-axis force sensor iscompleted, and the prototype of the sensor system is manufactured.
The calibration device for six-axis force sensor is manufactured and the static anddynamic calibration software is developed based on LabVIEW. The linearity,repeatability and hysteresis error of six-axis force sensor are derived. A multi-pointloading method to apply the loading force on each dimension step by step in the fullscales of force and torque is adopted. The static calibration experiments of sensorprototype are carried out, and the static performance indices of the sensor are obtained byprocessing the experimental data. The experimental result shows that the sensorprototype possesses good static performance.
Sources of measuring error of the parallel six-axis force sensor and the method toimprove the accuracy are studied. The influence of the axial deformation of themeasuring limbs to the measurement accuracy of parallel six-axis force sensor isanalyzed. The influence and compensation algorithm of the gravity of the robot’s endeffector when sensor applications are deduced. The influence of the pre-tightening forceto the measurement accuracy of pre-stressed six-axis force sensor is analyzed and amethod to reduce the measuring error by increasing the pre-tightening force is proposed.
By using screw theory and multi-degree-of-freedom system vibration mechanics, thevibration system simplified model of the double-layer and pre-stressed six-axis forcesensor is established, and the motion differential equation of the vibration system isdeduced. The response of the system in the initial excitation and the natural frequenciesof the sensor are obtained by solving the differential equations of motion. The dynamic calibration experiments are also carried out using the step signal response method, andthe natural frequency of the sensor is obtained. The experimental results are consistentwith the theoretical calculations and simulation.
The application research of six-axis force sensor is carried out based on two typicalmotion model of surface tracking and peg-in-hole assembly. The inadequacy of thesensor when measures the six-axis force online is pointed out by considering the threeforms of the generalized six-dimensional force/torque. The trajectories of the two motionmodels are planned, and the feedback control algorithm based on the measuringinformation of six-axis force sensor is deduced. The robot force control experimentalsystem is set up, and the control flow and motion control software based on the feedbackalgorithm are completed. Finally, the force feedback control experiments of surfacetracking and peg-in-hole assembly are carried out.
引文
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